Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 73E
Related questions
Question
![6. (a) Show that sinh (r) =
cosh(2.r) – 1
2
(b) Find the nth term of the following sequence
{1,8, 10, 26, 46, -..}
for all n 2 1.
(c) Define both absolute convergence and conditional convergence of a series.
7. (a) Given a,+1 = 2a, + an-1 and b+1 = 2b, + bn-1 for n 2 1, with ao = a1 = 1 and
bo = 0, bị = 1. It can be shown that (1+ v2)" = an + b, V2, Vn 2 0. Hence, prove
%3D
!!
that
a - b = (-1)".
2 - VA-x
(b) i) Compute lim
ii) Hence prove the limit in i) above by e-d definition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff46a0a5e-ce57-446d-b425-c6aafbe98a4c%2F0ee3295c-b920-45cf-bc20-03e2ddd4352b%2Fm5rvpsw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. (a) Show that sinh (r) =
cosh(2.r) – 1
2
(b) Find the nth term of the following sequence
{1,8, 10, 26, 46, -..}
for all n 2 1.
(c) Define both absolute convergence and conditional convergence of a series.
7. (a) Given a,+1 = 2a, + an-1 and b+1 = 2b, + bn-1 for n 2 1, with ao = a1 = 1 and
bo = 0, bị = 1. It can be shown that (1+ v2)" = an + b, V2, Vn 2 0. Hence, prove
%3D
!!
that
a - b = (-1)".
2 - VA-x
(b) i) Compute lim
ii) Hence prove the limit in i) above by e-d definition.
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